Abstract: The radial direction equation in the Klein-Gordon equation is calculated numerically, the condition and energy level of Yukawa potential bound states are discussed, and the function images of radial direction is given. The calculation result shows that when the parameter is small, the particles are in the ground state, not easy to be excited. It is also shown that when the parameter is very small, the particle bound state does not exist, and with the increase of the parameters V0, some energy states of low angular momentum disappear. Our analysis indicates that this is a result of centrifugal potential.

Key words: quantum mechanics, Yukawa potential, Klein-Gordon equation, bound state, energy level